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本文研究了线性时不变系统=Ax+Bu,y=Cx,引进状态反馈u=—Kx任意配置闭路极点问题。文中通过矩阵[sI—A]~(-1)B的右既约分解矩阵,导出了闭路系统特征方程的p×p维多项式矩阵行列式表示式(p=rankB)。利用这一表示式直接配置闭路极点,计算反馈矩阵K。文中同时给出了计算矩阵[sI—A]~(-1)B右既约分解矩阵的一种新算法。最后举例说明了它们的应用,并进一步讨论了K矩阵的灵活算法。
In this paper, we study the problem of closed-loop pole placement with linear time-invariant system = Ax + Bu, y = Cx and state feedback u = -Kx. In this paper, the p × p dimension polynomial matrix determinant (p = rankB) of the closed-loop system characteristic equation is derived from the right-approximation decomposition matrix of matrix [sI-A] ~ (-1) B. Use this expression to directly configure the closed-loop poles and calculate the feedback matrix K. In the meantime, a new algorithm for computing the right-approximation decomposition matrix of matrix [sI-A] ~ (-1) B is given. Finally, examples are given to illustrate their applications and to further discuss the flexible algorithm of K matrix.